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I was always taught that any accelerating charge produces radiation, but I don't think this condition is sufficient condition. For instance, any free charge on Earth is accelerated due to Earth orbiting the Sun but it doesn't produce radiation.

Qmechanic
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user34787
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  • "For instance any free charge on Earth is accelerated due to Earth orbiting the Sun but it doesn't produce charge" did you mean radiation? I'm sure someone will have an answer for you, but my hunch is that the answer is no because the Earth is following space-time curvature created by the gravitational field of the sun rather than accelerating. – SimpleLikeAnEgg Nov 26 '13 at 19:54
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    related: http://physics.stackexchange.com/q/70915/ , especially Ben Crowell's answer. – Art Brown Nov 27 '13 at 03:54
  • This article has a pretty good treatment of the subject. http://www.mathpages.com/home/kmath528/kmath528.htm – user6972 Nov 27 '13 at 09:20

2 Answers2

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In fact, an electric charge at rest on the Earth's surface is accelerated and this actually poses a challenge to the idea that uniformly accelerated charge radiates. I believe this is still an open question. For example:

One of the most familiar propositions of elementary classical electrodynamics is that "an accelerating charge radiates". In fact, the power (energy per time) of electromagnetic radiation emitted by a charged particle is often said to be strictly a function of the acceleration of that particle. However, if we accept the strong Equivalence Principle (i.e., the equivalence between gravity and acceleration), the simple idea that radiation is a function of acceleration becomes problematic, because in this context an object can be both stationary and accelerating. For example, a charged object at rest on the Earth's surface is stationary, and yet it's also subject to a (gravitational) acceleration of about 9.8 m/sec2. It seems safe to say (and it is evidently a matter of fact) that such an object does not radiate electromagnetic energy, at least from the point of view of co-stationary observers. If it did, we would have a perpetual source of free energy. Since the upward force holding the object in place at the Earth's surface does not act through any distance, the work done by this force is zero. Therefore, no energy is being put into the object, so if the object is radiating electromagnetic energy (and assuming the internal energy of the object remains constant) we have a violation of energy conservation.

A paper here proposes that uniformly accelerated charge does radiate but that the radiation is "beyond the horizon" for co-moving observers.

We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.

Alfred Centauri
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    so, how far would I need to put the radiation cells from the surface of the Earth to capture the radiation energy from the radiating charges? – lurscher Nov 27 '13 at 00:29
  • @lurscher, ???? – Alfred Centauri Nov 27 '13 at 00:33
  • @AlfredCentauri Is an electron orbiting the sun accelerating? There is no force being applied. Alternatively, if an electron were not orbiting, but just held in place by a force, is it not equivalent to acceleration? In other words an orbiting electron does not radiate, except in an accelerating reference frame? – SimpleLikeAnEgg Nov 27 '13 at 01:06
  • @SimpleLikeAnEgg, any particle, charged or otherwise, that is not on a geodesic is accelerated, i.e., an accelerometer attached to the particle gives a non-zero reading. Any particle in free-fall is inertial, i.e., the accelerometer reads zero. Does this answer your question? (it should). – Alfred Centauri Nov 27 '13 at 01:15
  • @AlfredCentauri Yes: an orbiting particle is on a geodesic and is therefore not accelerating. – SimpleLikeAnEgg Nov 27 '13 at 01:23
  • at one-g the Rindler horizon has a radius way smaller than the cosmological horizon, hence I can put cells beyond that distance and capture the radiation from the charges at Earth's surface, and have infinity energy. Don't you see something wrong with that? – lurscher Nov 27 '13 at 01:41
  • @lurscher, is it not the case that there are no comoving observers beyond the horizon? And, is it not the case the non-comoving observers detect radiation? – Alfred Centauri Nov 27 '13 at 02:44
  • beyond which horizon? the paper mentions the Rindler horizon only, which is not the same thing as the cosmological horizon – lurscher Nov 27 '13 at 07:27
  • @lurscher, I haven't mentioned a cosmological horizon anywhere in my previous comments. – Alfred Centauri Nov 27 '13 at 14:09
  • you are right, so if you put a cell outside that horizon, you can capture the radiated energy from the charges on the surface – lurscher Nov 27 '13 at 17:08
  • @lurscher, I'm not certain why you're focused on a cell outside the horizon. According to the paper, an inertial observer will observe radiation from the uniformly accelerated charge whether inside or outside the horizon. The paper distinguishes this from co-moving (with the charge) observers which do not observe radiation. And, as I wrote earlier, there are no co-moving observers outside the horizon. – Alfred Centauri Nov 27 '13 at 20:07
  • If this were to be the case, then you could get radiation energy out of any gravitational well with net charges. I'm not saying that it won't be, but it would be a bit weird. Although if the radiation happened to be thermal, I wonder if one can connect that to a Hawking radiation of charged black holes. Maybe any gravitational body with net charge would tend to evaporate, just like a black hole? – lurscher Nov 27 '13 at 22:46
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The charge accelerated by the Earth gravity does not emit any radiation,follows from transforming to a frame of reference in which the charge is stationary and applying relativistic requirement that the behavior of the charge including whether or not it radiates,cannot depend on the frame of reference from which it is viewed.

user34793
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  • That is what is unclear for me (I am not familiar with General relativity). So I can always distinguish between acceleration due to gravity and "normal acceleration"? And what about the Earth orbiting the Sun? Does it produce any radiation (Free charges on Earth)? – user34787 Nov 27 '13 at 10:49
  • Not really !my knowledge of our planet is limited,but what I can say is that the Earth hardly or never emits charged particles,however it does emit radiation in the sense of thermal radiation..if the Earth emitted charged particles,which I am sure would be radioactive,we would be exposed to radiation almost everyday,many creatures would've even been mutated. – user34793 Nov 27 '13 at 11:30
  • This is simplistic and wrong. There are lots of subtleties involved. For example, it is not necessarily true that the existence of radiation can be defined in a way that is independent of the frame of reference, including noninertial frames. –  Jul 30 '17 at 16:29